How do you solve #(3/4)^(2x) = 64/27#?

1 Answer
ali ergin
Mar 28, 2016

#x=-5,3188416645#

Explanation:

#(3/4)^(2x)=64/27#
#(3/4)^(2x)=2^6/3^3#

#3^(2x)/4^(2x)=2^6/3^3#

#3^(2x)*3=4^(2x)*2^6#

#3^(2x+1)=2^(4x)*2^6#

#3^(2x+1)=2^(4x+6)#

#log 3^(2x+1)=log 2^(4x+6)#

#(2x+1)*log 3=(4x+6)*log 2#
#log 3=0,47712125773#
#log 2=3010299957#
#(2x+1)*0,47712125773=(4x+6)*0,3010299957#
#0,9542425094x+0,47712125773=1,2041199827x+1,806179974#
#0,2498774733x=-1,329058716#

#x=-5,3188416645#

Related questions
See all questions in Logarithmic Models
Impact of this question
1500 views around the world
You can reuse this answer
Creative Commons License